Analysis of Australian Twin Data by using Shared Frailty Models based on Reversed Hazard

A. Pandey¹ , Lalpawimawha ² , P.K. Misra³

Section:Research Paper, Product Type: Journal-Paper
Vol.6 , Issue.2 , pp.91-98, Apr-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.9198

Online published on Apr 30, 2019

Copyright © A. Pandey, Lalpawimawha , P.K. Misra . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this paper, we propose shared frailty models based on reversed hazard rate with exponentiated moment exponential distribution as baseline distribution. The Bayesian approach of Markov Chain Monte Carlo (MCMC) technique was employed to estimate the parameters involved in the models. A simulation study also performed to compare the true value and the estimated value of the parameters. Comparison with the non-parametric model also done by using Bayesian comparison techniques . We apply to the Australian twin data set and better model is suggested.

Key-Words / Index Term :
Bayesian comparison technique, Exponentiated moment exponential distribution, MCMC, Reversed hazard, Shared frailty model

References :
[1] P.K. Andersen, O. Borgan, R.D. Gill, N. Keiding, ”Statistical Methods Based on Counting Processes”, NewYork, Springer Verlag, 1993.
[2] A. Pandey, Lalpawimawha , S. Bhushan, P.K. Misra, “Correlated Gamma Frailty Model Based on Logistic Exponential Baseline Distribution”, International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol. 5, pp. 170-176, 2018.
[3] R.E. Barlow, A.W. Marshal, F. Proschan, F,” Properties of the probability distribution with monotone hazard rate”, Ann. Math. Stat. . Vol. 34, pp. 375-389, 1963.
[4] H.W. Block, T.H. Savits, H. Singh, H,” On the reversed hazard rate function”, Probab. Eng. Inf. Sci., Vol. 12, pp. 69-90, 1998.
[5] D.G. Clayton, “A model for association in bivariate life tables and its applications to epidemiological studies of familial tendency in chronic disease incidence”, Biometrica. Vol. 65,pp. 141-151, 1978.
[6] D.D. Hanagal, A. Pandey,“Gamma shared frailty model based on reversed hazard rate”, Communications in Statistics - Theory and Methods. Vol. 45(7), pp. 2071-2088, 2016.
[7] L. Duchateau, P. Janssen, “The Frailty Model”, Springer, New York, 2008.
[8] D.L. Duffy, N.G. Martin, J.D. Mathews,“Appendectomy in Australian twins”, Aust. J. Hum. Genet., Vol. 47(3),pp. 590-592, 1990.
[9] A. Gelman, D.B. Rubin,”A single series from the Gibbs sampler provides a false sense of security”,In Bayesian Statistics 4 (J. M. Bernardo, J. 0.Berger, A. P. Dawid and A. F. M. Smith, eds.), Oxford: Oxford Univ. Press, pp. 625-632, 1992.
[10] J. Geweke,“Evaluating the Accuracy of Sampling-Based Approaches to the Calculation of Posterior Moments", In Bayesian Statistics 4 (eds. J.M. Bernardo, J. Berger, A.P. Dawid and A.F.M. Smith), Oxford: Oxford University Press, pp. 169-193, 1992.
[11] U. Gurler,“Bivariate Estimation With Right-Truncated Data”,Journal of the American Statistical Association, Vol. 91(435), pp. 1152-1165, 1996.
[12] D.D. Hanagal,”Modeling Survival Data Using Frailty Models”, Boca Raton,Chapman& Hall/CRC, 2011.
[13] S.A. Hasnain, Z. Iqbal, M. Ahmad,”On exponentiated moment exponential distribution”,Pakistan Journal of Statistics, Vol. 31(2), pp. 267-280, 2015.
[14] J.G. Ibrahim, M.H. Chen, D. Sinha, “ Bayesian Survival Analysis”,Springer, Verlag, 2001.
[15] R.A. Kass, A.E. Raftery,”Bayes` factor”,Journal of the American Statistical Association, Vol. 90,pp. 773-795, 1995.
[16] S. Kheiri, A. Kimber, M.R. Meshkani,”Bayesian analysis of an inverse Gaussian correlated frailty model”, Computational Statistics and Data Analysis, Vol. 51,pp. 5317-5326, 2007.
[17] J.F. Lawless,“Statistical Models and Methods for Lifetime Data”, (2nd ed.),New Jersey: John Wiley and Sons, 2003.
[18] S.K. Sahu, D.K. Dey, H. Aslanidou, D. Sinha,”A Weibull regression model with gamma frailties for multivariate survival data”, Life time data analysis, Vol. 3,pp. 123- 137, 1997.
[19] P.G. Sankaran, V.L. Gleeja,”On bivariate reversed hazard rates”, J. Jpn. Stat. Soc., Vol. 10,pp. 181-198, 2006.
[20] P.G. Sankaran, V.L. Gleeja,“Proportional reversed hazard and frailty models”, Metrika , Vol. 68,pp. 333-342, 2008.
[21] C.A. Santos, J.A. Achcar,”A Bayesian analysis for multivariate survival data in the presence of covariates”, Journal of Statistical Theory and Applications, Vol. 9,pp. 233-253, 2010.
[22] D. Sengupta, A.K. Nanda,“The proportional reversed hazards regression model”,Statistical Theory and Applications, Vol. 18,pp. 461-476, 2011.
[23] A. Wienke,“Frailty Models in Survival Analysis” New York, CRC Press, 2010.